A natural number is a number like 0, 1, 2, 3, 4, 5, 6, … which can be used to represent the count of an object. The set of natural numbers is \(\mathbb N.\) Not all sources include 0 in \(\mathbb N.\)
Thanks to their simplicity, natural numbers are often the first mathematical concept taught to children. Natural numbers are equipped with a notion of($2 + 3 = 5$ and so on) and ($2 \cdot 3 = 6$ and so on), these are among the first mathematical operations taught to children.
Despite their simplicity, the natural numbers are a ubiquitous and useful mathematical object. They’re quite useful for counting things. They represent all the possible cardinalities of finite sets. They’re also a useful , in that numbers can be used to all sorts of data. Almost all of modern mathematics can be built out of natural numbers.
Add a “formalization” lens with the Peano axioms. I recommend at least one page with just the raw Peano axioms (and very little prose), and another gentler introduction sort of like http://bit.ly/29glDrR and http://bit.ly/29nKYAL, albeit more to-the-point and probably without going all the way up to non-standard number territory.
- Graham's number
A fairly large number, as numbers go.
- A googolplex
A moderately large number, as large numbers go.
- A googol
A pretty small large number.
- Prime number
The prime numbers are the “building blocks” of the counting numbers.
Mathematics is the study of numbers and other ideal objects that can be described by axioms.